Unformatted text preview: x 2 + y 2 + z 2 = 4 x and inside the paraboloid of revolution x = y 2 + z 2 . Hint: Sketch the surface. 17.6c. Find an equation for the tangent plane to the surface parameterized by r ( u, v ) = ± u 2 , v 2 , uv ² at the point (4 , 4 ,4) . Sketch a graph of the surface and the tangent plane. Use MAPLE if you wish. 17.6d. Please do Problems 1318 of § 17.6 in Stewart’s Multivariable Calculus . 17.6e. Sketch the surface described by the parameterization r ( u, v ) = ± 2 u cos( v ) , 2 u sin( v ) , v ² for 1 ≤ u ≤ 4 and v ∈ [ π, 2 π ] . Find the area of this surface. 17.6f. Find a parametric representation for the upper half of the ellipsoid 4 x 2 + 2 y 2 + z 2 = 1 . 17.6g. Find a parametric representation for that part of the sphere of radius 12 centered at the origin that lies above the cone z = ² x 2 + y 2 ....
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This note was uploaded on 04/01/2008 for the course MATH 215 taught by Professor Fish during the Winter '08 term at University of Michigan.
 Winter '08
 Fish
 Multivariable Calculus

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